Can you think of a single example that: 1) Posits new conjectures 2) Proves those conjectures 3) Those conjectures can be used to formulate new conjectures tha

Can you think of a single example that: 1) Posits new conjectures 2) Proves those conjectures 3) Those conjectures can be used to formulate new conjectures that conform to items 1-3? I've read a great deal of smalltalk literature, and I can't recall any papers that would qualify. There's plenty of empirical exploration of ambiguous hypothesis, but nothing that actually provides anyone in the field anything on which they could actually build.